{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "095b0666",
   "metadata": {},
   "source": [
    "# Example 11: Encouraging linearity\n",
    "\n",
    "### In cases where we don't know how deep we should set KANs to be, one strategy is to try from small models, grudually making models wider/deeper until we find the minimal model that performs the task quite well. Another strategy is to start from a big enough model and prune it down. This jupyter notebook demonstrates cases where we go for the second strategy. Besides sparsity along width, we also want activation functions to be linear ('shortcut' along depth)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef047a0f",
   "metadata": {},
   "source": [
    "### Tricks\n",
    "\n",
    "There are two relevant tricks: \n",
    "\n",
    "(1) set the base function 'base_fun' to be linear; \n",
    "\n",
    "(2) penalize spline coefficients. When spline coefficients are zero, the activation function is linear."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91301ca0",
   "metadata": {},
   "source": [
    "### Case 1: 1D function $f(x)={\\rm sin}(\\pi x)$. Although we know a [1,1] KAN suffices, we suppose we don't know that and use a [1,1,1,1] KAN instead."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77f9e16d",
   "metadata": {},
   "source": [
    "### without trick"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c881665b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 6.78e-04 | test loss: 7.09e-04 | reg: 1.29e+00 : 100%|██| 20/20 [00:03<00:00,  5.28it/s]\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "# create dataset f(x,y) = sin(pi*x). This task can be achieved by a [1,1] KAN\n",
    "f = lambda x: torch.sin(torch.pi*x[:,[0]])\n",
    "dataset = create_dataset(f, n_var=1)\n",
    "\n",
    "model = KAN(width=[1,1,1,1], grid=5, k=3, seed=0)\n",
    "\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "201ceacf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13c725a5",
   "metadata": {},
   "source": [
    "### with tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a22ffff3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 4.40e-03 | test loss: 4.22e-03 | reg: 3.35e+00 : 100%|██| 20/20 [00:03<00:00,  5.78it/s]\n"
     ]
    }
   ],
   "source": [
    "from kan import *\n",
    "\n",
    "# create dataset f(x,y) = sin(pi*x). This task can be achieved by a [1,1] KAN\n",
    "f = lambda x: torch.sin(torch.pi*x[:,[0]])\n",
    "dataset = create_dataset(f, n_var=1)\n",
    "\n",
    "# set base_fun to be linear\n",
    "model = KAN(width=[1,1,1,1], grid=5, k=3, seed=0, base_fun=lambda x: x)\n",
    "\n",
    "# penality spline coefficients\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=1e-4, lamb_coef=10.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c82c8db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af370a4c",
   "metadata": {},
   "source": [
    "### Case 2: 2D function $f(x,y)={\\rm exp}({\\rm sin}(\\pi x)+y^2)$.  We know a [2,1,1] KAN represents it. Let's suppose we don't know about that and use a [2,3,3,3,1] KAN instead."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdba8357",
   "metadata": {},
   "source": [
    "### without tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5920bdaf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 8.02e-02 | test loss: 8.01e-02 | reg: 1.24e+01 : 100%|██| 20/20 [00:33<00:00,  1.70s/it]\n"
     ]
    }
   ],
   "source": [
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "\n",
    "model = KAN(width=[2,3,3,3,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "26af5d19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 28 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b0316bee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune()\n",
    "model(dataset['train_input'])\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca1c5e86",
   "metadata": {},
   "source": [
    "### with tricks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1f82e8c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 8.19e-02 | test loss: 7.77e-02 | reg: 1.37e+01 : 100%|██| 20/20 [00:29<00:00,  1.47s/it]\n"
     ]
    }
   ],
   "source": [
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "\n",
    "model = KAN(width=[2,3,3,3,1], grid=5, k=3, seed=0)\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_coef=1.0);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e09861b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 28 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "31ee6172",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = model.prune()\n",
    "model(dataset['train_input'])\n",
    "model.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
